Download 1 Organic Molecules and Decoherence Experiments in a Molecule

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Organic Molecules and Decoherence
Experiments in a Molecule Interferometer
M. Arndt, L. Hackermüller, K. Hornberger, and A. Zeilinger
Institut für Experimentalphysik
Universität Wien
Boltzmanngasse 5
A-1090 Wien, Austria
1.1 Classical behaviour from quantum physics
One of the basic objectives in the foundations of physics is to understand the
detailed circumstances of the transition from pure quantum effects to classical
appearances. This field has gained an even increased attention because of the
fact that quantum phenomena on the mesoscopic or even macroscopic scale
promise to be useful for future technologies, such as in lithography with clusters and molecules, quantum computing or highly sensitive quantum sensors.
In the present work we describe one specific type of quantum effect, namely
the wave-particle duality and the requirements to observe this phenomenon.
The wave-nature of matter has been known for the last 80 years and it finds
daily technological confirmation and application in the material sciences which
use electron diffraction, electron holography or neutron diffraction to investigate surfaces or bulk material.
Here we shall focus on the extension of matter-wave experiments towards
more massive, more complex and larger quanta, ranging from carbon clusters,
over biologically relevant organic molecules to fullerene derivatives.
The non-observability of quantum wave effects in our daily world can be
described by various complementing arguments: The first set of theories assumes an objective reduction of the wavefunction, which may be described by
a non-linear extension of the Schrödinger equation [8, 18]. The second set of
theories takes the unitarity of the Schrödinger equation as the central element
of quantum physics and tries to explain the appearance of classical phenomena
within the well-established linear dynamics.
The simplest argument of this category is, that quantum effects are often
simply too small to be observable. For instance any diffraction pattern of a
human being would take a diffraction experiment larger than the size of the
known universe to separate the interference fringes to a measurable distance.
The de Broglie wavelength of a walking human being is actually below the
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M. Arndt, L. Hackermüller, K. Hornberger, and A. Zeilinger
Planck length of 10−35 m — and one can currently only speculate about the
meaning of any wave physics with dimensions below that scale.
Fig. 1.1. The fullerene C70 is composed of 70 carbon atoms in an oval shape
(left). Tetraphenylporphyrin C44 H30 N4 (TPP, m=614 amu) is composed of four
tilted phenyl rings attached to a planar porphyrin structure (middle). The largest
dimension measures about 2 nm and the aspect ratio (height to width) is roughly
seven. The fluorinated fullerene C60 F48 (m=1632 amu) (right) is a deformed buckyball surrounded by a shell of 48 fluorine atoms. This molecule exists in different
isomers and only one structure with D2 symmetry is shown here [20].
Now, while this dynamical argument certainly holds, it seems there is
another mechanism which limits the appearance of quantum effects even
for smaller objects under real-world conditions: Decoherence theory, which
started to flourish about two decades ago [21, 22, 14, 9, 2, 23], states that
isolated quantum systems may always maintain their quantum nature —
independent of their size or mass — but that it becomes increasingly difficult
to guarantee this isolation for large objects. The qualitative idea is that any
coupling between the system and the environment will lead to an entanglement of the two. Any coherence in the quantum system will be rapidly diffused
into the complex environment and will therefore no longer be observable. As
soon as the environment can distinguish between different quantum states of
the system, i.e., as soon as which-state information becomes accessible to the
outer world, a superposition of these states is no longer observable.
A simple example is given by the fact that a human being is in perpetual
interaction with its environment through collisions with the surrounding air
molecules. It is very hard to quantitatively follow the loss of coherence in such
a macroscopic body, since about 1027 molecules impinge on a human body per
second. Decoherence is thus expected to occur on time scales well below any
available experimental resolution.
However, as we shall discuss below, macromolecule interferometry allows
us to study the effect of collisions quantitatively as one important origin of
the transition from the quantum to the classical: Molecules in a high-vacuum
environment exhibit pure quantum properties if properly prepared. Since the
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background gas pressure may be well controlled by the experimentalist, quantum effects may be turned gradually and in a controlled way into classical
appearances.
1.2 Coherence experiments
The quantum wave nature of material objects is well established for small
particles. But the conceptual dissonance between the local character of the
‘particle’ and the non-local character of the ‘wave’ seems to strike our common
sense even stronger if we consider objects which can already be clearly seen
as isolated particles under a microscope. This is the case for nanometer sized
molecules and clusters like the fullerenes, porphyrins or fullerene derivatives
which are shown in Fig. 1.1 (left to right).
Fullerenes, named after the geodesic domes created by the architect Buckminster Fuller [16], were discovered only in 1985 by Kroto and coworkers [15].
The ‘buckyball’ C60 and the ‘bucky-rugbyball’ C70 (Fig. 1.1, left) were the first
macromolecules for which wave-particle duality was demonstrated [1] mainly
because they can be easily vaporized, they are very stable, and they can be
efficiently detected using laser ionization [17]. In addition to these practical
reasons they offer many similarities to bulk material: They possess bulk-like
excitations such as phonons, excitons and plasmons. They may be regarded
as their own internal heat bath, and they are known to emit thermal electrons
or thermal photons or even diatomic molecules when they are heated to sufficiently high temperatures. In that sense they are a very good approximation
to a classical body on the nanoscale. They have a mass of 840 amu and a
diameter of roughly 1 nm. They are rigid and highly symmetric.
In contrast to the fullerenes the second species used in our experiments,
the porphyrins, are very abundant in nature. The porphyrin structure can
be found in the core of a heme molecule or in chlorophyll and since a metal
atom inside the porphyrin structure gives blood its red color and chlorophyll
its green appearance, porphyrins are often referred to as the ‘colors of life’.
The particles used in our experiments are derivatives of this porphyrin structure: They are enlarged by four tilted phenyl rings, which lead to the full
name tetraphenylporphyrin (TPP, Fig. 1.1, center). Although even successful
interference experiments with porphyrins are obviously far from proving the
relevance of quantum mechanics in the living world, they are nevertheless an
interesting twist in an experiment on the foundations of quantum physics:
The diameter of the TPP molecule — measured by the core to core distance
of the outermost nuclei — is three times as large as that of C70 , it is flat instead of nearly spherical, it has dangling phenyl rings sticking out and the
polarizability is much more anisotropic than in the case of the fullerenes.
Finally, we have also performed matter wave interferometry with the fluorinated fullerene C60 F48 . It has the shape of a deformed buckyball with
48 fluorine atoms covalently bound to the outer shell. The diameter of this
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M. Arndt, L. Hackermüller, K. Hornberger, and A. Zeilinger
molecule is in between that of the pure buckyball and the porphyrins, but the
mass of 1632 amu is about twice the mass of C70 . It represents the current
record in mass, complexity and number of atoms contained in a single quantum object in a matter wave experiment1 . The fluorinated fullerenes exist
in several isomers of different symmetry which were probably present in all
configurations.
Fig. 1.2. Setup of the Talbot–Lau interferometer: hot, thermal molecules enter a
near-field interferometer, which consists of three identical gold gratings. The first
grating represents an array of slit sources which imprint the required coherence
onto the uncollimated, spatially incoherent molecular beam. The second grating
images this slit source onto the plane of the third grating. The third grating serves
as a mask for the detection of the interference fringes: Only molecules positionsynchronized with the grating will pass the structure and may be observed in the
following detector, composed of laser ionization and ion counting [5].
The best way to prove an assumed wave-like phenomenon is to observe interference. Although in earlier experiments with C60 molecules far-field diffraction was an ideal tool for this purpose because of its conceptual simplicity,
all experiments described here were performed in a near-field interferometer
of the Talbot–Lau type which has been proposed by Clauser et al. [7, 6]
and which has only recently been applied to large molecules [5, 4]. There are
two main reasons for this choice: Firstly, the three grating arrangement allows us to work with an uncollimated, spatially incoherent molecule source.
This is essential for the biomolecules and large clusters, since typical source
intensities are much below those of atomic or fullerene beams. Secondly, the
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It is important not to confuse the macroscopically occupied field of a Bose–
Einstein condensate (BEC) with the single many-body wavefunction of a complex
molecule: the de Broglie wavelength of a BEC is always that of a single atom,
while the molecular λdB is determined by all participating atoms.
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dimension requirements (grating constant, and grating separation) are less
severe in a near-field interferometer compared to far-field diffraction or farfield interferometry. This is seen by the fact that the grating constant in our
present near-field interferometer is 1µm, while it had to be ten times smaller
for the previous far-field experiments [1].
The experimental setup is shown in Fig. 1.2. Molecules are sublimated in
an oven at the maximum allowed temperature before the onset of molecular
decomposition, i.e., at 890 K for C70 , 690 K for TPP and 560 K for C60 F48 .
The molecules fly into the high vacuum chamber and traverse the interferometer, before they enter the detector. In all C70 experiments the detector
consists of a laser ionization stage and subsequent ion counting. This method
is very efficient (ηion ∼ 10%) [17] but highly molecule specific. Most large
organic molecules would rather fragment than ionize. For the porphyrins
and fluorofullerenes we therefore employ electron impact ionization, which
also leads to the formation of positive ions. However, the efficiency is reduced to ηion ∼ 10−4 . Since electron impact is not molecule selective we
add a quadrupole mass selection stage to separate the porphyrins and fluorofullerenes from air molecules and contaminations in the vacuum chamber.
The interferometer itself consists of three gold gratings, with a grating
constant of 990 nm and an open fraction of about f = 0.48, i.e., open gaps of
about 470 nm. The gratings are separated by a distance of L = 38 cm [11].
250
counts / s
200
150
100
50
0
58
59
60
position of 3rd grating (mm)
61
46
47
48
position of 3rd grating (mm)
Fig. 1.3. Left: Interference pattern recorded for porphyrin molecules at 166 m/s.
The interference contrast of 38% is in good agreement with quantum mechanical
expectation and in clear disagreement with the classical value of 13%. The interferogram was recorded over a few minutes. Right: The same experiment performed
with C60 F48 and recorded over three hours. The picture consists of an average of
13 ‘low-noise’ single scans which were selected by the magnitude of their frequency
noise (not by the value of the frequency). [10].
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M. Arndt, L. Hackermüller, K. Hornberger, and A. Zeilinger
The longitudinal, i.e., spectral coherence length lc = λ2 /∆λ inside the
oven is determined by the velocity spread in the source and it is only about
1.5 times larger than the de Broglie wavelength, which lies for all particles and
velocities in the range of 2 . . . 5 × 10−12 m. Both the de Broglie wavelength
and the coherence length are thus 500 . . . 1000 times smaller than the size
of the molecules themselves! The transverse coherence is equally small when
the molecules leave the oven, and in that sense it is fully justified to speak
of well-localized particles in the preparation stage. However, each slit in the
first grating boosts the transverse coherence length of the molecular beam
at the position of the second grating by about six orders of magnitude [3].
The indistinguishable passage through two or more slits leads to quantum
interference behind the second grating, in particular to the formation of a
molecular density pattern with the same period as the diffraction structure
in about the distance of the Talbot length LT = g 2 /λdB behind the grating.
Contributions from different slits in the first grating add up incoherently but in
phase. The molecular density distribution can be probed using a third grating
with again the same period, which is shifted transversely to the molecular
beam. Whenever the molecular structure and the gold grating are in phase,
most molecules will pass it and reach the detector. If the grating is slightly
shifted, the count rate is reduced. The interference pattern is thus revealed
by scanning the mask across the molecule beam.
Fig. 1.3 (left) shows typical high-contrast interference fringes of porphyrin.
The contrast of 38% is in good agreement with the theoretically expected
value and it is about a factor of three higher than the classically expected
shadow contrast. Both the classical and the quantum calculation include the
van der Waals interaction between the molecules and the 500 nm thin grating
walls [11]. The quantum mechanical wave nature can further be proved by the
way the interference pattern changes with the de Broglie wavelength: We can
vary the molecule velocity and thus de Broglie wavelength. Since the Talbot
length depends on λdB , also the interference contrast is effected by the varying
velocity and we find very good agreement between theory and experiment for
all velocity classes (see [11]).
For the fluorinated fullerenes the same experiment was repeated. Fig. 1.3
(right) shows the result for C60 F48 . The contrast of 27% is clearly above
the classical expectation of 12% but still below the best possible quantum
interference contrast of 37%. We attribute this difference mainly to vibrations
on the level of a few ten nanometers which affect slow molecules more than fast
ones. C60 F48 had a most probable speed of 100 m/s while the TPP interference
pattern was recorded for a mean molecular velocity of 166 m/s. The vibration
hypothesis is further supported by the fact that slow fullerenes can also show
a decrease in fringe visibility by about 30% and also by dedicated vibration
experiments [19]. The second reason is the large technical background noise
in these experiments in addition to the low count rates and correspondingly
long integration times. Both effects tend to reduce the interference contrast.
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Fig. 1.4. Idea of the decoherence experiment: The originally delocalized molecules
may be well localized through interactions with the environment. Collisions with
background gas molecules start to become relevant at pressures above 10−7 mbar.
The gas pressure representing the environment can be well controlled by the experimentalist.
1.3 Decoherence experiments
Having shown a high level of coherence in experiments with large molecules,
it is now interesting to investigate the limit of matter wave interferometry
due to the coupling between the quantum object and its environment. These
studies have again been performed with C70 to make use of the much higher
count rates and better statics compared to the TPP and C60 F48 experiments.
One can imagine many different couplings between a particle and its environment. Collisions and radiative interactions will be the most frequent and
most natural processes in our macroworld, and here we shall focus on collisions in particular.
fullerene
molecule in the superposition of two position
left A right
eigenstates C70
, C70
will get entangled
with a gaseous environment,
since the state of an incident gas particle g will be changed depending on
the position of the fullerenes:
right coll. 1 left left right right left
ψ = √1 C70
+ C70
⊗ g −→ √ C70 gscat + C70 gscat
2
2
Any ‘measurement’ on the state of the scattered gas particle, by further interactions with other gas molecules or the walls, can be regarded as an effective
measurement
fullerene path. If the scattered gas states
are
distinguish right
leftof the
right left
C70
C
gscat
able, i.e., gscat
= 0, interference between
and
can no
70
longer be observed and the superposition state ψ has effectively collapsed.
A more detailed description of the collisional decoherence rate in collision
experiments has been given in [13, 12]. The main result with respect to our
investigation is that we expect an exponential loss of the interference contrast
with increasing pressure of the residual gas
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M. Arndt, L. Hackermüller, K. Hornberger, and A. Zeilinger
2Lσeff
V (p) = V0 exp −
p = V0 exp(−p/pv ).
kB T
(1.1)
In Fig. 1.5 we show the experimental result for fullerenes in interaction
with Argon atoms at base pressures between 10−8 . . . 10−6 mbar. We find the
predicted single-exponential decay, and the theoretical decay curve fits the
experiment without free parameter, except for the contrast at p = 0 mbar,
which is also influenced by vibrations or other effects that are independent
of the base pressure. We emphasize that the exponential decay in Fig. 1.5 is
a clear signature of decoherence. In the case of simple absorption it would
be the beam intensity that shows an exponential decrease, while the visibility would remain constant. Note also that decoherence theory describes the
experiment not only qualitatively but quantitatively. The experiment allowed
even falsification of an incorrect localization rate that differs by a factor of 2π
(see the discussion in [12]).
Let us note that there are two equivalent ways of viewing the decoherence
process observed in the experiment. On the one hand one can say that the
change in the state of the scattered gas particle is strong enough to obtain
full information on the position of a fullerene by a single collision. On the
other hand one can view the fullerene in the momentum representation. Then
the recoil during a single collision translates the momentum distribution such
that the final interference pattern is shifted substantially with respect to the
unscattered case. Since the collision angles turn from a quantum superposition
into a broad distribution once the gas particle is ‘measured’ by the environment, the summation of many randomly shifted single-molecule interference
patterns again washes out the total fringe pattern. It is worth noting that
in our experiment a sizeable number of the collisions between fullerenes and
residual gas particles lead to kicks out of the detection range and therefore
to loss. These events do not contribute to the reduction of the fringe contrast. Only small angle collisions, with θ ∼ 1 mrad, leave the molecules inside
the interferometer while they still dephase the interference fringes. We can
extrapolate the numerical data which we obtained in similar decoherence experiments with different residual gases to predict the feasibility of experiments
with even larger objects than the porphyrins or fluorofullerenes. It turns out
that even for objects with masses around 107 amu the 1/e-decoherence pressure will ‘only’ be ∼ 10−10 mbar, a value which can still be reached with
standard laboratory equipment [10]. Collisional decoherence — although very
efficient on the macro-scale — is thus still far from being a limit to interferometry for objects with sizes below 10 nm. However, the influence of radiative
interactions, of quasi-static interactions with fluctuating or strongly dispersive potentials for molecules with a large electric polarizability, electric or
magnetic dipole moment still remains to be investigated.
Quantum optics with macromolecules has only begun. We foresee many
important developments and future improvements concerning the sources for
neutral macromolecules, more efficient detection schemes and novel types of
1 Organic Molecules and Decoherence Experiments
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Fig. 1.5. Interference fringe visibility for C70 fullerenes interacting with Argon
gas at various pressures in the interferometer. A clear single-exponential decay is
observed as expected from decoherence theory.
interferometers. Applications will range from fundamental studies of decoherence to the potential use of molecule lithography and nanotechnology.
Acknowledgements We thank our colleagues Björn Brezger, Elisabeth
Reiger and Stefan Uttenthaler, for their contribution to the described experiments. This work has been supported by the Austrian Science Foundation
(FWF), within the project START Y177 and SFB F1505, as well as by the
European networks HPRN-CT-2000-00125, HPRN-CT-2002-00309.
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